The American Heritage Dictionary summarizes the weekday homage to Germanic gods thusly:
The names of the days of our week are based on the ancient astrological notion that the seven celestial bodies (sun, moon, Mars, Mercury, Jupiter, Venus, Saturn) revolving around the stationary Earth influenced events on Earth and that each the bodies controlled the first hour of the day named after it. The system was brought into Hellenistic (hi of Troy!) Egypt from Mesopotamia. In 321 AD, Constantine the Great grafted the system onto the Roman calendar and declared the sequence: Dies Solis, Dies Lunae, Dies Martis, Dies Mercurii, Dies Iovis, Dies Veneris, and Dies Saturni. The Roman system was adopted throughout western Europe, and in the Germanic languages, including Old English, four of the Roman gods were converted into the corresponding Germanic gods. So: Sunnandaeg, Monandaeg, Tiwesdaeg (the god Tiu, like Mars, was a god of war), Wodensdaeg (the god Woden, like Mercury, was quick and eloquent), Thunresdaeg (the god Thunor (OE) or Thor (ON), like Jupiter, was lord of the sky), Frigedaeg (the goddess Frigg, like Venus, was the goddess of love), and Saeternesdaeg.
The same source lists "Tiu" as the Germanic god of war and the sky, and says its source is "OE Tiw. See deiw-" The Indo-European roots index entry for "deiw-" tells us that diew means to shine, and in many derivatives, sky, heaven, god. It also says that "Tiwes" is the genitive of "Tiu." [finally, the answer!]
Important derivatives of "deiw" include Tuesday, deity, divine, jovial, July, Jupiter, Zeus, dial, diary, dismal, journey and psychedelic. (Ha! I didn't expect to tie all those terms together today. Thanks, Max, for getting me started on this.